What does "They'll run overseas'?" mean?

Question

'Aren't you English?' said Dan. 'We heard you singing just now.' 'Aha! That was the Sussex side o' me. Dad he married a French girl out o' Boulogne, and French she stayed till her dyin' day. She was an Aurette, of course. We Lees mostly marry Aurettes. Haven't you ever come across the saying:

'Aurettes and Lees,
Like as two peas.
What they can't smuggle,
They'll run overseas'?

'Then, are you a smuggler?' Una cried; and, 'Have you smuggled much?' said Dan. Mr Lee nodded solemnly.

This is from "Rewards and Fairies" "Brother Square-Toes" by Kipling. http://pinkmonkey.com/dl/library1/digi300.pdf

What do the lines below mean? What they can't smuggle, They'll run overseas'?

Does they mean like this? What they can't smuggle will go(fly) over the seas?

I am glad if some one kindly teach me.

Answer 1

It's a joke.

To smuggle a commodity is to import it illegally—at the period and in the context of the story, primarily to bring brandy and tobacco from France into England without paying excise taxes.

Run here is used transitively, with the sense "transport quickly", as when we ask a friend with a car "Can you run me to the grocery store?" To run a commodity over seas (or overseas) is to transport it across the seas to a foreign country.

So "What they can't smuggle they'll run over seas" means, literally

Any commodity they can't smuggle, they export.

That joke is that since the Aurettes and Lees live on opposite sides of the English channel, what the Lees "smuggle"—import—is what the Aurettes "run over seas"—export.

"The Aurettes used mostly to run the stuff across from Boulogne, and we Lees landed it here and ran^† it up to London Town, by the safest road."

So the rhyme is equivalent to saying that the two families' business consists entirely of illegal shipping.

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^† Note, again, transitive run, meaning transport.